Quantal Density Functional Theory

Abstract

Quantal density functional theory (Q-DFT) is a local effective potential energy theory [1]–[8] along the lines of Slater theory [9, 10] and traditional Hohenberg-Kohn-Sham density functional theory [11]–[14]. The basic idea, in common with Kohn-Sham density functional theory (KS-DFT) to be described more fully in the next chapter, is the construction of a model system of noninteracting Fermions whereby the density ρ(rt)/ρ(r) and energy E(t) / E equivalent to that of Schrödinger theory is obtained. Since these Fermions are noninteracting, their effective potential energy υs(rt) / υs(r) is the same. The corresponding quantum mechanical operator representative of this potential energy is therefore multiplicative, and it is said to be a local operator. We refer to this model as the S system, S being a mnemonic for ‘single Slater’ determinant. Within Q-DFT the potential energy of the noninteracting Fermions is defined explicitly in terms of the various electron correlations that must be accounted for by the S system. It is also possible to construct in the framework of Q-DFT, S systems such that the density and energy of both Hartree and Hartree-Fock theories is obtained. In a following chapter we will describe a Q-DFT whereby a system of noninteracting Bosons — the B system — is constructed such that the density and energy equivalent to that of Schrödinger theory is once again determined.